Find electric field (in $N / C$ ) at point $P$ in vector form due to point charges kept as shown (Here charge $Q = 0.25 μ C$ )

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$104 \hat{i} + 72 \hat{j} + 72 \hat{k}$

$108 \hat{i} - 72 \hat{j} - 72 \hat{k}$

$72 \hat{i} + 108 \hat{j} - 72 \hat{k}$

$108 \hat{i} + 72 \hat{j} - 70 \hat{k}$

answer is B.

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Detailed Solution

$\vec{r_{1}} = (3 - 0) \hat{i} + (0 - 4) \hat{j} + (0 - 0) \hat{k} \vec{r_{1}} = 3 \hat{i} - 4 \hat{j} a n d r_{1} = \sqrt{3^{2} + 4^{2}} = 5 \vec{r_{2}} = (3 - 0) \hat{i} + (0 - 0) \hat{j} + (0 - 4) \hat{k} \vec{r_{2}} = 3 \hat{i} - 4 \hat{k} a n d r_{2} = \sqrt{3^{2} + 4^{2}} = 5$

$\vec{E_{1}} = k \frac{Q}{r_{1}^{2}} \hat{r_{1}} = (9 \times 10^{9}) \frac{(25 \times 10^{- 8})}{5^{2}} \frac{(3 \hat{i} - 4 \hat{j})}{5} = 18 (3 \hat{i} - 4 \hat{j}) = 54 \hat{i} - 72 \hat{j} N / C S i m i l a r l y, \vec{E_{2}} = \frac{k Q}{r_{2}^{2}} \hat{r_{2}} = (9 \times 10^{9}) \frac{(25 \times 10^{- 8})}{5^{2}} \frac{(3 \hat{i} - 4 \hat{k})}{5} = 18 (3 \hat{i} - 4 \hat{k}) = 54 \hat{i} - 72 \hat{k} N / C$